Specifies whether singular vectors are to be computed in compact form, as follows:

= 0: Compute singular values only.

= 1: Compute singular vectors of upper bidiagonal matrix in compact form.

The maximum size of the subproblems at the bottom of the computation tree.

The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array

d

.

Specifies the column dimension of the bidiagonal matrix.

If

sqre

= 0

: the bidiagonal matrix has column dimension

m

=

n

If

sqre

= 1

: the bidiagonal matrix has column dimension

m

=

n

+ 1

.

Array,

DIMENSION

(

n

). On entry,

d

contains the main diagonal of the bidiagonal matrix.

Array,

DIMENSION

(

m

- 1 ). Contains the subdiagonal entries of the bidiagonal matrix. On exit,

e

is destroyed.

The leading dimension of arrays

u

,

vt

,

difl

,

difr

,

poles

,

givnum

, and

z

.

ldu

≥

n

.

The leading dimension of arrays

givcol

and

perm

.

ldgcol

≥

n

.

Workspace array,

DIMENSION

(6

n

+(

smlsiz

+1)

2

)

.

Workspace array,

Dimension

must be at least (7

n

).

On exit

d

, if

info

= 0

, contains the singular values of the bidiagonal matrix.

Array,

DIMENSION

(

ldu

,

smlsiz

) if

icompq

=1

.

Not referenced if

icompq

= 0

.

If

icompq

= 1

, on exit,

u

contains the left singular vector matrices of all subproblems at the bottom level.

Array,

DIMENSION

(

ldu

,

smlsiz

+1 ) if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit,

vt

' contains the right singular vector matrices of all subproblems at the bottom level.

Array,

DIMENSION

(

n

) if

icompq

= 1

and

DIMENSION

(1) if

icompq

= 0

.

If

icompq

= 1

, on exit,

k

(

i

) is the dimension of the

i

-th secular equation on the computation tree.

REAL

for

slasda

DOUBLE PRECISION

for

dlasda

.

Array,

DIMENSION

(

ldu

,

nlvl

),

where

nlvl

= floor(log

2

(

n

/

smlsiz

))

.

Array,

DIMENSION

(

ldu

, 2

nlvl

) if

icompq

= 1

and

DIMENSION

(

n

) if

icompq

= 0

.

If

icompq

= 1

, on exit,

difl

(1:

n

,

i

) and

difr

(1:

n

,2

i

-1) record distances between singular values on the

i

-th level and singular values on the (

i

-1)-th level, and

difr

(1:

n

, 2i ) contains the normalizing factors for the right singular vector matrix. See

?lasd8

for details.

Array,

DIMENSION

(

ldu

,

nlvl

) if

icompq

= 1

and

DIMENSION

(

n

) if

icompq

= 0

. The first

k

elements of

z

(1,

i

) contain the components of the deflation-adjusted updating row vector for subproblems on the

i

-th level.

Array,

DIMENSION

(

ldu

, 2*

nlvl

)

if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit,

poles

(1, 2

i

- 1) and

poles

(1, 2

i

) contain the new and old singular values involved in the secular equations on the

i

-th level.

Array,

DIMENSION

(

n

) if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit,

givptr

(

i

) records the number of Givens rotations performed on the

i

-th problem on the computation tree.

Array,

DIMENSION

(

ldgcol

, 2*

nlvl

)

if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit, for each

i

,

givcol

(1, 2

i

- 1) and

givcol

(1, 2

i

) record the locations of Givens rotations performed on the

i

-th level on the computation tree.

Array,

DIMENSION

(

ldgcol

,

nlvl

) if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit,

perm

(1,

i

) records permutations done on the

i

-th level of the computation tree.

Array

DIMENSION

(

ldu

, 2*

nlvl

) if

icompq

= 1

, and not referenced if

icompq

= 0

. If

icompq

= 1

, on exit, for each

i

,

givnum

(1, 2

i

- 1) and

givnum

(1, 2

i

) record the

C

- and

S

-values of Givens rotations performed on the

i

-th level on the computation tree.

Array,

DIMENSION

(

n

) if

icompq

= 1

, and

DIMENSION

(1) if

icompq

= 0

.

If

icompq

= 1

and the

i

-th subproblem is not square, on exit,

c

(

i

) contains the

C

-value of a Givens rotation related to the right null space of the

i

-th subproblem.

Array,

DIMENSION

(

n

)

icompq

= 1

, and

DIMENSION

(1) if

icompq

= 0

.

If

icompq

= 1

and the

i

-th subproblem is not square, on exit,

s

(

i

) contains the

S

-value of a Givens rotation related to the right null space of the

i

-th subproblem.

= 0: successful exit.

< 0: if

info

= -

i

, the

i

-th argument had an illegal value

> 0: If

info

= 1

, an singular value did not converge